Acoustic metamaterials for sound focusing and confinement

被引:267
作者
Guenneau, Sebastien
Movchan, Alexander
Petursson, Gunnar
Ramakrishna, S. Anantha
机构
[1] Univ Liverpool, Dept Math Sci, Liverpool L69 3BX, Merseyside, England
[2] CNRS, Inst Fresnel, UMR 6133, F-13397 Marseille 20, France
[3] Indian Inst Technol, Dept Phys, Kanpur 208016, Uttar Pradesh, India
关键词
NEGATIVE REFRACTION; INDEX; CHECKERBOARDS; ABSORPTION;
D O I
10.1088/1367-2630/9/11/399
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We give a theoretical design for a locally resonant two-dimensional cylindrical structure involving a pair of C-shaped voids in an elastic medium which we term as double 'C' resonators (DCRs) and imbedded thin stiff bars, that displays the negative refraction effect in the low frequency regime. DCRs are responsible for a low frequency band gap which hybridizes with a tiny gap associated with the presence of the thin bars. Using an asymptotic analysis, typical working frequencies are given in closed form: DCRs behave as Helmholtz resonators modeled by masses connected to clamped walls by springs on either side, while thin bars behave as a periodic bi-atomic chain of masses connected by springs. The discrete models give an accurate description of the location and width of the stop band in the case of the DCR and the first two dispersion bands for the periodic thin bars. We then combine our asymptotic formulae for arrays of DCR and thin-bars to design a composite structure that displays a negative refraction effect and has a negative phase velocity in a frequency band, and thus behaves in many ways as a negative refractive acoustic medium (NRAM). Finite element computations show that at this frequency, a slab of such NRAM works as a phononic flat superlens whereas two corners of such NRAM sharing a vertex act as an open resonator and can be used to confine sound to a certain extent.
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页数:18
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